Generation of Lower Harmonic Magnetosonic Waves through Nonlinear Wave-Wave Interactions

Although magnetosonic waves in the Earth's magnetosphere have been well understood by the linear theory, low harmonic magnetosonic waves, which often lack of free energy, can be unusually present. By employing a 1-D particle-in-cell simulation model, we have investigated the generation of those unusual lower harmonic magnetosonic waves in a plasma containing a proton ring distribution. In our simulation, the higher harmonic magnetosonic waves (from~9Ω_h to ~12Ω_h) are firstly excited due to the unstable proton ring, which can be well explained by the linear theory. Several lower harmonic magnetosonic waves (below 5Ω_h), which well separates away from the higher harmonics, soon appear in the system. Those lower harmonics, which do not have any positive linear growth rates, can be generated by a nonlinear mechanism. The bicoherence analysis demonstrates that there is a strong phase coupling among the unusual lower harmonic magnetosonic waves and the magnetosonic waves generated due to the proton ring, supporting the idea that the lower harmonic waves could be driven by the wave-wave couplings of the generated magnetosonic waves. This wave-wave coupling generation mechanism is further confirmed by another two simulations, where two or three pump magnetosonic waves are initially injected. The lower-frequency waves, that is, the fundamental wave and its second harmonic, are also successfully reproduced due to the nonlinear coupling of pump magnetosonic waves. Our simulations not only propose a potential generation mechanism of unusual lower harmonic magnetosonic waves in the Earth's magnetosphere, but also give some new insights on the evolution of magnetosonic spectra.